Question

Let f(x)=(x-2)/((sqrtx)-(sqrt2)), if x does NOT equal 2 and f(x)=k if x=2.

Then f is continuous everywhere in its domain if k=

Answer 1

(x-2)/(√x-√2)
= [(√x-√2)(√x+√2)]/(√x-√2)
= √x+√2
for all x≠2

So, if k=2√2 f is continuous everywhere.